[Corribus]

I'm looking to calculate (or at least estimate) the ionic strength for a citric acid solution with pH ~ 2.5. Specifically, I'd like to compare it to the ionic strength of a monoprotic acid solution of identical pH. However I'm having a surprisingly difficult time doing it.

I could show you my work but it more or less amounts to a lot of scribbled out stuff on a piece of notebook paper.

Any tips?

[Babcock_Hall]

I thought that the first pK_a was between 2 and 3, and the next two were between 4 and 5, and between 6 and 7, respectively.  The third practical pK_a is the one most strongly affected by ionic strength, at least in the approximation with which I am familiar.  My only thought would be to ignore the second and third pK_a, and calculate the ionic strength as if neutral and mono anionic forms were the only ones present, as a first approximation.

[Corribus]

pKa values are 3.13, 4.76, and 6.39.

I estimated it quick and dirty as follows. For shorthand, I called the mono-cation citrate ion "A", the di-cation "B" and the trication "C". I figure that based on these pKa values, there are approximately 42 times as many A's in solution as B's, and about 42 times as many B's as there are C's. If there are a total of 0.003162 M protons in the solution (from the pH), there are an identical number of total dissociation events. Based on proportions, I estimated 1.749E-9 M C, 7.35E-5 M B, and 3.086E-3 M A at equilibrium. I plug these all into the ionic strength equation and I get a value of 3.168E-3 M, versus 3.162E-3 for a monoprotic acid of same pH. So, very little difference.

Now, how awful were those assumptions?? Go ahead and laugh, I can take it. 

[Borek]

Matter of having correct tools

Note: both solutions have pH of 2.50, but concentrations were found by trial and error, so these are not identical pH values (just the difference is below the last digit of the H⁺ activity).

[Corribus]

Yes, having the right tools helps! I guess I wasn't too far off with my back of the envelope (literally) estimate.

[Corribus]

Hey Borek - Does your amazing tool allow you to predict these values at other temperatures?

[Borek]

Hey Borek - Does your amazing tool allow you to predict these values at other temperatures?

If you know dpKa/dT, yes. Unfortunately, I don't have these for citric acid (but you can add them manually to the database if you happen to find them). Other things (like Kw(T), and dependence of the A constant in the Debye-Huckel equation on temperature), are taken care of automatically (as explained here: http://www.chembuddy.com/?left=Buffer-Maker&right=buffer-calculation ).